Fluctuation of the download network

Abstract

The scaling behavior of fluctuation for a download network which we have investigated a few years ago based upon Zhang's Encophysics web page has been presented. A power law scaling, namely $\sigma \sim < f> ^ \alpha $ exists between the dispersion $\sigma$ and average flux $<f>$ of the download rates. The fluctuation exponent $\alpha$ is neither 1/2 nor 1 which was claimed as two universal fluctuation classes in previous publication, instead it varies from 1/2 to 1 with the time window in which the download data were accumulated. The crossover behavior of fluctuation exponents can be qualitatively understood by the external driving fluctuation model for a small-size system or a network traffic model which suggests congestion as the origin.